Hello, and thank you very much in advance for any help provided, I am grateful!!!

I am not completely stupid when it comes to computers; I'd say I'm 'a bit above average' if you were to look at the general population, but I'm still not completely hip to all the lingo, so please bear with me if I have to ask a stupid question

I'll start with the history/symptoms ---

Purchased computer new less than a year ago (Nov 2012)In the last month or so, when I go to restart the computer, often it would not boot. Usually would boot on the 2nd or 3rd try.Today, it would not boot at all (the computer itself would turn on as well as the monitor, but only black screen.)I turned off the power strip, unplugged/replugged everything just to make sure something wasn't loose or a squished chord.Tried to reboot. Black screen again.Reboot #2 worked.Everything started as normal, except when I went to open Google Chrome, my regular 'dashboard' page popped up - as usual - and then a second page popped up, without me doing/clicking anything - it was hotcleaner . com. It showed a bar saying it was checking my system and I closed it really fast.I closed chrome, deleted all web history, cookies, etc.Opened chrome again to come to this website.Got a red popup from avast:

I ran a check on Spybot - Search & Destroy - I'll include some of the report you may find useful below. Please let me know if I missed anything (and my apologies if I didn't post the right parts, or repeated them...) or can answer any more questions in assisting your help!!